Interacting fluctuations and the two-loop order parameters of the strong-coupling negative- U Hubbard model

Abstract

The effective field theory that describes the interaction of fluctuations of the attractive Hubbard model in the strong-coupling limit is formulated and applied to obtain the two-loop results for the order parameters of the model at low temperatures and in the leading singularities near two dimensions. Starting from a Grassmann functional integral representation of the strong-coupling model on the restricted fermionic Hilbert space, which corresponds to the anisotropic spin- 1 2 Heisenberg quantum antiferromagnet, we derive the effective field theory up to fifth order in the bosonic fluctuation fields. The loop corrections of the order parameters for superconductivity and charge ordering and of the chemical potential are evaluated including both the singular planar phase fluctuations and the out-of-plane fluctuations, which become soft at half band-filling. The results are in agreement with the scaling behaviour expected from the corresponding XY and Heisenberg limits of the O( n) non-linear σ-model.